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JEE Mains · Maths · STD 12 - 13. probability

Let \(A\) and \(E\) be any two events with positive probabilities:
Statement \(- 1\): \(P\left( {E/A} \right) \geq P\left( {A/E} \right)P\left( E \right)\)
Statement \(-2\) : \(P\left( {A/E} \right) \geq P\left( {A \cap E} \right)\)

  1. A Both the statements are true
  2. B Both the statements are false
  3. C Statement \(-1\) is true, Statement \(- 2\) is false
  4. D Statement \(-1\) is false, Statement \(-2\) is true
Verified Solution

Answer & Solution

Correct Answer

(A) Both the statements are true

Step-by-step Solution

Detailed explanation

Let \(A\) and \(E\) be any two events with positive probabilities. Consider statement-\(1\): \(\mathrm{P}(\mathrm{E} / \mathrm{A}) \geq \mathrm{P}(\mathrm{A} / \mathrm{E}) \mathrm{P}(\mathrm{E})\)…
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